If 2nC3 : nC2 = 44 : 3, find n.

Q13 of 118 Page 18

If ²ⁿC₃ : ⁿC₂ = 44 : 3, find n.

Given:

⇒

We know that

And also n! = n(n – 1)(n – 2)…………2.1

⇒

⇒ 2 × (2n – 1) × 2 = 44

⇒ 2n – 1 = 11

⇒ 2n = 12

⇒

⇒ n = 6

∴ The value of n is 6.

If ²⁸C_2r : ²⁴C_{2r – 4} : 225 : 11, find r.

If ⁿC₄, ⁿC_5, and ⁿC₆ are in A.P., then find n.

If ¹⁶C_r = ¹⁶C_{r + 2}, find ^rC₄.

If α = ^mC₂, then find the value of ^αC₂.